Assessment Alignment Curriculum,

instruction, and assessment

What does alignment look like?

Curriculum

Assessment

Instruction

Instructional tasks are connected to curriculum expectations

Formative assessment is embedded in instruction

Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

Starting with curriculumTeachers use practices and procedures that are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students; (1 of 7 fundamental principles in Growing Success)

“Assessment is the process of gathering information from a variety of sources (including assignments, demonstrations, projects, performances, and tests) that accurately reflects how well a student is achieving the curriculum expectations in a course.” (OME, 2005a, p. 17)

Consider

Content expectations

Mathematical processes

NCTM Assessment Standards Mathematics Standard

Assessment should reflect the mathematics that all students need to know and be able to do.

Inferences Standard Assessment should promote valid inferences about

mathematics learning.

What does alignment look like?

Curriculum

Assessment

Instruction

Instructional tasks are connected to curriculum expectations

Formative assessment is embedded in instruction

Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

What does alignment look like?

Curriculum

Assessment

Instruction

Instructional tasks are connected to curriculum expectations

Formative assessment is embedded in instruction

Specific assessment tasks resemble instructional tasks and focus on achievement of curriculum expectations

Processes

Content

Mathematical Activity

Investigating

solving

graphing

Collecting data

describing

Determining, through investigation

comparing

explaining

representing

modeling

Drawing diagrams

Creating

tables

Mathematical Processes

• Problem solving• Reasoning and

proving• Reflecting• Selecting Tools and

Strategies• Connecting• Representing• Communicating

Implications for assessment?

A test along will not do!!

The complexity of mathematical actions need to be assessed in a variety of ways Observation Performance tasks Presentations Journals Investigations Conferencing and dialogue

Examining curriculum expectations

Grade 1, measurement

Students will:

estimate, measure, and describe length, area, mass, capacity, time, and temperature, using non-standard units of the same size(OME, 2005a, p. 35).

What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

Examining curriculum expectations

Grade 4, geometry and spatial sense

Students will:

construct three-dimensional figures, using two-dimensional shapes construct a three-dimensional figure from a picture or

model of the figure, using connecting cubes (e.g., use connecting cubes to construct a rectangular prism);

construct skeletons of three-dimensional figures, using a variety of tools (e.g., straws and modelling clay, toothpicks and marshmallows, Polydrons), and sketch theskeletons;

What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

Examining curriculum expectations

Grade 7, measurement

Students will:

determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g. parallelograms, trapezoids), and generalize to develop the formula (i.e., Volume = area of base x height) (OME, 2005a, p. 101).

What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

Examining curriculum expectations

Grade 9, geometry and measurement

Students will:

verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

Examining curriculum expectations

Grade 11, Functions course

Students will:

determine the formula for the sum of an arithmetic or geometric series, through investigation using a variety of tools (e.g., linking cubes, algebra tiles, diagrams, calculators)and strategies (e.g., patterning; connecting the steps in a numerical example to the steps in the algebraic development), and apply the formula to calculate the sum of a given number of consecutive terms (OME, 2007, p. 51)What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

At your tableWork with a partner(s) and decide on one of the grade expectations presented.

Discuss What might instructional activity look like that addresses this expectation?

How would we assess students with respect to this expectation?

Dilemmas In my coaching role, I often hear the question, "This

teaching through problem solving is fine and I can see the benefits to my students. How do I assess it? How do I keep track of everything?" This is a very good question because if teachers struggle with this aspect of teaching through PS, then they will be unlikely to persist with it because the assessment is too unwieldy.

I find that it is a real challenge for teachers to identify the types of questions in relation to the achievement chart in mathematics.

Dilemmas in alignment

In a discussion on collaborative assessment, teachers who have students engage in collaborative problem solving tasks as part of instruction wonder whether and how they can assess students in such a collaborative setting.

This led to a discussion of

The value of aligning instruction and assessment

Whether one is “allowed” to do this for a summative task

What this might look like in practice

Conceptual

Political

Pedagogical

What do you think?

Alignment: A complex issue